Fractional differentiability of nowhere differentiable functions and dimensions

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the `critical order' 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/ local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals.Comment: minor changes, 19 pages, Late

Conserved charges for gravity with locally AdS asymptotics

A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.Comment: 5 pages, 2 Columns, revtex. Last version for Phys. Rev. Let

Holder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.Comment: 20 pages, Late

Quantum Cosmology and Open Universes

Quantum creation of Universes with compact spacelike sections that have curvature $k$ either closed, flat or open, i.e. $k=\pm1,0$ are studied. In the flat and open cases, the superpotential of the Wheeler De Witt equation is significantly modified, and as a result the qualitative behaviour of a typical wavefunction differs from the traditional closed case. Using regularity arguments, it is shown that the only consistent state for the wavefunction is the Tunneling one. By computing the quantum probabilities for the curvature of the sections, it is shown that quantum cosmology actually favours that the Universe be open, $k=-1$. In all cases sufficient inflation $\sim 60$ e-foldings is predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.Comment: 11 pages, Revtex, 7 figures. Accepted for publication in PRD. New material and important corrections added in response to referee's repor

Nuclear Clusters as a Probe for Expansion Flow in Heavy Ion Reactions at 10-15AGeV

A phase space coalescence description based on the Wigner-function method for cluster formation in relativistic nucleus-nucleus collisions is presented. The momentum distributions of nuclear clusters d,t and He are predicted for central Au(11.6AGeV)Au and Si(14.6AGeV)Si reactions in the framework of the RQMD transport approach. Transverse expansion leads to a strong shoulder-arm shape and different inverse slope parameters in the transverse spectra of nuclear clusters deviating markedly from thermal distributions. A clear ``bounce-off'' event shape is seen: the averaged transverse flow velocities in the reaction plane are for clusters larger than for protons. The cluster yields --particularly at low $p_t$ at midrapidities-- and the in-plane (anti)flow of clusters and pions change if suitably strong baryon potential interactions are included. This allows to study the transient pressure at high density via the event shape analysis of nucleons, nucleon clusters and other hadrons.Comment: 38 pages, 9 figures, LaTeX type, eps used, subm. to Phys. Rev.

Dyson summation without violating Ward identities and the Goldstone-boson equivalence theorem

In contrast to the conventional treatment of gauge theories, in the background-field method the Ward identities for connected Green functions are not violated by Dyson summation of self-energies in finite orders of perturbation theory. Thus, Dyson summation does not spoil gauge cancelations at high energies which are ruled by the Goldstone-boson equivalence theorem. Moreover, in the background-field method the precise formulation of the equivalence theorem in higher orders (including questions of renormalization) is simplified rendering actual calculations easier. Finally, the equivalence theorem is also formulated for the Standard Model with a non-linearly realized scalar sector and for the gauged non-linear $\sigma$-model.Comment: 26 pages, latex, complete ps-file available via anonymous ftp from ftp://ftp.physik.uni-wuerzburg.de/pub/preprint/1996/WUE-ITP-96-002.ps, reference added and some comments on Ref.[6] modifie

Genetic research: the role of citizens, public health and international stakeholders

Background: Genetic research has become an indispensable instrument for medical research, and the subjects involved have both divergent and convergent interests. Objective: The possibility of having more detailed genetic information undoubtedly offers benefits for the health of the subject, but could also pose risks and make the subject vulnerable to discrimination. Methods: The scientific community has viewed very favorably the public health utility of family history, in which data from a family whose members suffer from chronic pathologies is collected and filed, in order to develop a sort of “stratification of family risk.” Even though in the last decade the scientific and juridical literature has contributed greatly to the topic of biobanks, the perplexities that continue to surround this theme give the idea that current ethical protocols on research are inadequate. Results: Researchers, citizens, International stakeholders, mass media, Public Health and Governments play a key role in genetic research. It is obvious that the methods used for genetic research do not present intrinsic risks; they are much less dangerous than other activities of diagnosis and research. Before authorizing a research project, it is important to reflect on the responsibility and transparency of the studies to be conducted, and on the impact they may have on the interests of public health. Conclusion: We believe that the highest priority need is to develop a common language on the theme, as is the case in the sphere of clinical experimentation where rules of good clinical practice, albeit at times conflicting, have led to uniform convergences in the scientific world on the points to be actuated

Obesity prevention and personal responsibility: the case of front-of-pack food labelling in Australia

<p>Abstract</p> <p>Background</p> <p>In Australia, the food industry and public health groups are locked in serious struggle for regulatory influence over the terms of front-of-pack food labelling. Clear, unambiguous labelling of the nutritional content of pre-packaged foods and of standardized food items sold in chain restaurants is consistent with the prevailing philosophy of 'personal responsibility'. An interpretive, front-of-pack labelling scheme has the capacity to encourage healthier patterns of eating, and to be a catalyst for improvements in the nutritional quality of food products through re-formulation. On the other hand, the strength of opposition of the Australian Food and Grocery Council to 'Traffic Light Labelling', and its efforts to promote a non-interpretive, voluntary scheme, invite the interpretation that the food industry is resistant to any reforms that could destabilise current (unhealthy) purchasing patterns and the revenues they represent.</p> <p>Discussion</p> <p>This article argues that although policies that aim to educate consumers about the nutritional content of food are welcome, they are only one part of a broader basket of policies that are needed to make progress on obesity prevention and public health nutrition. However, to the extent that food labelling has the capacity to inform and empower consumers to make healthier choices - and to be a catalyst for improving the nutritional quality of commercial recipes - it has an important role to play. Furthermore, given the dietary impact of meals eaten in fast food and franchise restaurants, interpretive labelling requirements should not be restricted to pre-packaged foods.</p> <p>Summary</p> <p>Food industry resistance to an interpretive food labelling scheme is an important test for government, and a case study of how self-interest prompts industry to promote weaker, voluntary schemes that pre-empt and undermine progressive public health regulation.</p

Theories of schizophrenia: a genetic-inflammatory-vascular synthesis

BACKGROUND: Schizophrenia, a relatively common psychiatric syndrome, affects virtually all brain functions yet has eluded explanation for more than 100 years. Whether by developmental and/or degenerative processes, abnormalities of neurons and their synaptic connections have been the recent focus of attention. However, our inability to fathom the pathophysiology of schizophrenia forces us to challenge our theoretical models and beliefs. A search for a more satisfying model to explain aspects of schizophrenia uncovers clues pointing to genetically mediated CNS microvascular inflammatory disease. DISCUSSION: A vascular component to a theory of schizophrenia posits that the physiologic abnormalities leading to illness involve disruption of the exquisitely precise regulation of the delivery of energy and oxygen required for normal brain function. The theory further proposes that abnormalities of CNS metabolism arise because genetically modulated inflammatory reactions damage the microvascular system of the brain in reaction to environmental agents, including infections, hypoxia, and physical trauma. Damage may accumulate with repeated exposure to triggering agents resulting in exacerbation and deterioration, or healing with their removal. There are clear examples of genetic polymorphisms in inflammatory regulators leading to exaggerated inflammatory responses. There is also ample evidence that inflammatory vascular disease of the brain can lead to psychosis, often waxing and waning, and exhibiting a fluctuating course, as seen in schizophrenia. Disturbances of CNS blood flow have repeatedly been observed in people with schizophrenia using old and new technologies. To account for the myriad of behavioral and other curious findings in schizophrenia such as minor physical anomalies, or reported decreased rates of rheumatoid arthritis and highly visible nail fold capillaries, we would have to evoke a process that is systemic such as the vascular and immune/inflammatory systems. SUMMARY: A vascular-inflammatory theory of schizophrenia brings together environmental and genetic factors in a way that can explain the diversity of symptoms and outcomes observed. If these ideas are confirmed, they would lead in new directions for treatments or preventions by avoiding inducers of inflammation or by way of inflammatory modulating agents, thus preventing exaggerated inflammation and consequent triggering of a psychotic episode in genetically predisposed persons